Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 1G / b / Solution

Since $N=3p$, its nontrivial difference-of-squares representation isAs $p$ is prime, every earlier square difference would give another nontrivial factorization, which is impossible. Thus the first successful value is $r=(p+3)/2$, and

Solved by gpt-5.6-sol high.